Goldstone Boson Normal Coordinates

Abstract

The phenomenon of spontaneous symmetry breaking is well known. It is known to be accompanied with the appearance of the 'Goldstone boson'. In this paper we construct the canonical coordinates of the Goldstone boson, for quantum spin systems with short range as well as long range interactions.

Goldstone bosons in Josephson junctions

“…These oscillations together with the Goldstone boson disappear if the SSB disappears. In [7] one was able to construct explicitly the normal coordinates of these new particles called Goldstone particles. In particular for mean field systems such as the BCS-model [8], the Overhauser model [9], a spin density wave model [10], the anharmonic crystal model [13], and the jellium model [11], one has constructed these Goldstone boson normal coordinates.…”

“…Section 3 is devoted to the study of the appearance of Goldstone bosons in the junction, due to the interaction of the two bulk superconductors and a direct consequence of the gauge symmetry breaking. We apply the general result of [7] where one finds the general explicit construction of the normal I N × N II N × N Figure 1: Two superconductors wit a contact surface coordinates of the Goldstone boson as a consequence of the spontaneous symmetry breaking which appears in our model. The Goldstone bosons of the bulk superconductors can also be found in that paper.…”

Metastability in the BCS model

“…The phase of the order parameter φ, defined by λ = |λ|e iφ , φ ∈ [0, 2π], remains free to choose. This leads to an infinite degeneracy of the states in the superconductive regime and is due to spontaneous symmetry breaking [10,11]. As this phase becomes important in the remainder of this article, it will from now on explicitly be labelled, i.e.…”

“…The exit-time is the time necessary to leave the initial state on the basis of having reached the maximum value of the observable under consideration. In the BCS-model, the observables which are invariant under the gauge transformation group of the broken symmetry [10][11][12], come over as relevant observables. They all exhibit metastable relaxation and all have the same exit-time.…”

Central limit theorems for the large-spin asymptotics of quantum spins

“…Typically, this happens in the presence of a spontaneously broken continuous symmetry, and the macroscopic quantum fluctuations present in such a system are the well-known Goldstone bosons [1]. A general theory of Goldstone bosons using non-commutative central limit theorems was presented in [17].…”